White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles

Tiange Xu and Tusheng Zhang

Stochastic Processes and their Applications, 2009, vol. 119, issue 10, 3453-3470

Abstract: In the first part of this paper, we prove the uniqueness of the solutions of SPDEs with reflection, which was left open in the paper [C. Donati-Martin, E. Pardoux, White noise driven SPDEs with reflection, Probab. Theory Related Fields 95 (1993) 1-24]. We also obtain the existence of the solution for more general coefficients depending on the past with a much shorter proof. In the second part of the paper, we establish a large deviation principle for SPDEs with reflection. The weak convergence approach is proven to be very efficient on this occasion.

Keywords: Parabolic; obstacle; problems; Stochastic; partial; differential; equations; with; reflection; Skeleton; equations; Weak; convergence; Large; deviation; principles (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (14)

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